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- W1515776875 abstract "We investigate relations on elements in $C^{*}$-algebras, including $*$-polynomial relations, order relations and all relations that correspond to universal $C^{*}$-algebras. We call these $C^{*}$-relations and define them axiomatically. Within these are the compact $C^{*}$-relations, which are those that determine universal $C^{*}$-algebras, and we introduce the more flexible concept of a closed $C^{*}$-relation. In the case of a finite set of generators, we show that closed $C^{*}$-relations correspond to the zero-sets of elements in a free $sigma$-$C^{*}$-algebra. This provides a solid link between two of the previous theories on relations in $C^{*}$-algebras. Applications to lifting problems are briefly considered in the last section." @default.
- W1515776875 created "2016-06-24" @default.
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- W1515776875 date "2010-09-01" @default.
- W1515776875 modified "2023-10-11" @default.
- W1515776875 title "$C^*$-Algebra relations" @default.
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- W1515776875 doi "https://doi.org/10.7146/math.scand.a-15142" @default.
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